Joint distribution is an advanced logistics organization model for improving the quality and efficiency of express logistics industry and achieve high-quality development of logistics, but the distribution of common profit has always been a key obstacle to the effective development of joint distribution. Based on the background of green and low-carbon, this paper explores a fairer and more reasonable profit distribution scheme. The profit game between the government and the two types of member enterprises is analyzed. By focusing on how the government plays a role in inducing the joint distribution alliance to bring the green and low-carbon requirements into the profit distribution, the strategy evolution process of the three parties, the factors affecting the profit distribution and the stability of alliance are discussed through the establishment of "government-member enterprise A-member enterprise B" tripartite evolutionary game model. Finally, the evolutionary game model is numerically simulated based on system dynamics. It is found that: (1) It is necessary for the government to guide and motivate the alliance to create internal incentives and constraints. The effect of government subsidies and rewards to member enterprises is greater than the penalties for member enterprises. (2) The member enterprises are likely to conspire together to defraud government subsidies and rewards, carry out "free riding" and other speculative activities, which makes it necessary for the government and the alliance to establish supervision mechanism, information disclosure mechanism, and property rights protection system. (3) The willingness of member enterprise to positively cooperate will increase with the increase of the additional benefit coefficient, the proportion of profit distribution and the importance of environmental benefit factor; and will decrease with the increase of the cost of promoting green distribution operations.